If a principal amount becomes Rs 2,07,360 in 4 years with a compound interest rate of `20%` per annum, then what is the value of principal amount?

Options

A. Rs 111000
B. Rs 110000
C. Rs 120000
D. Rs 100000

Answer

To find the principal amount when the amount becomes Rs 2,07,360 in 4 years at a compound interest rate of 20% per annum, we can use the formula for compound interest:

\[ A = P \left(1 + \frac{R}{100}\right)^n \]

Where:
- \( A \) = Amount after time \( n \)
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( n \) = Number of years

Given:
- \( A = 2,07,360 \)
- \( R = 20\% \)
- \( n = 4 \)

### Step 1: Substitute the values into the formula

\[ 2,07,360 = P \left(1 + \frac{20}{100}\right)^4 \]

### Step 2: Simplify the equation

\[ 2,07,360 = P \left(1 + 0.2\right)^4 \]

\[ 2,07,360 = P \left(1.2\right)^4 \]

### Step 3: Calculate \( (1.2)^4 \)

\[ (1.2)^4 = 1.2 \times 1.2 \times 1.2 \times 1.2 \]

Calculating step by step:
- \( 1.2 \times 1.2 = 1.44 \)
- \( 1.44 \times 1.2 = 1.728 \)
- \( 1.728 \times 1.2 = 2.0736 \)

Thus, \( (1.2)^4 = 2.0736 \).

### Step 4: Substitute back into the equation

\[ 2,07,360 = P \times 2.0736 \]

### Step 5: Solve for \( P \)

\[ P = \frac{2,07,360}{2.0736} \]

### Step 6: Perform the division

Calculating:
\[ P = \frac{2,07,360}{2.0736} = 1,00,000 \]

### Final Answer

The principal amount is Rs 1,00,000.

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